This document has nls (non-linear least squares) regression fits using the LOG-NORMAL functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) Biomass growth vs. stand biomass relationships. We calculated the biomass of each FIA plot by summing alive tree biomass (as reported by FIA). Stand age is also reported by FIA, using tree-core age estimates from two trees from the dominant size class of the FIA plot.
We considered the following Log-Normal functional form \(B = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(StdAge /c \right)} {d} \right]} ^2 \right)\), where \(B\) is the plot biomass, \(StdAge\) is the stand age at time of biomass measurement, \(\Delta PDSI\) is the difference in the 9-month annual average PDSI (excluding the winter months, i.e., January-September) over the FIA plot biomass interval, which is defined as the measurement time minus 10 years and a 30-year climate normal from 1960 to 1989, and \(yr\) is the measurement year. Free parameters are: \(ge\): biomass growth enhancement over time, \(\phi\): the effect of climate dryness on stand biomass, \(a\): the y-intercept of the curve, \(a +b\): the peak value of \(B\), \(c\): the \(StdAge\) value at peak \(B\), and \(d\): the log-normal curve shape parameter.
Model selection is used to determine the best fitting models, which is implemented in two parts. The first part selected the best model form using the base model (i.e., excluding phi), and \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or the difference in the Palmer drought severity index from June - August for the 10 years preceding the biomass measurement and the 1960-1989 period).
model 1: simple model \(B = (1 + (yr-1990) \cdot ge/100) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(B_{t1} /c \right)} {d} \right]} ^2 \right)\)
model 2: phi model \(B = (1 + (yr-1990) \cdot ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left(a + b \cdot \exp{ - \left[ \frac{ \log \left(B_{t1} /c \right)} {d} \right]} ^2 \right)\)
Note:
This analysis uses ALL available plot biomass data
which includes the following plot-based filtering criteria:
Below the model fitting procedure is implemented by ecoprovince:
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 9936 2501.4
## 2 9935 2488.4 1 13.012 51.95 6.107e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 107696.3
## 2 2 107646.5
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.241234 0.106391 -2.267 0.0234 *
## phi 0.048121 0.006438 7.474 8.41e-14 ***
## a 28.841474 1.209812 23.840 < 2e-16 ***
## b 131.423715 4.344807 30.248 < 2e-16 ***
## c 126.036776 5.371817 23.463 < 2e-16 ***
## d 1.102377 0.040252 27.387 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5005 on 9935 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 30368 10474
## 2 30359 10474 9 0.31831 0.1025 0.9996
## model AIC
## 1 1 316275.7
## 2 2 316195.9
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.11401 0.06468 1.763 0.078 .
## phi 0.00000 0.00308 0.000 1.000
## a 14.45284 0.39879 36.242 <2e-16 ***
## b 92.71935 1.75123 52.945 <2e-16 ***
## c 128.41078 4.06060 31.624 <2e-16 ***
## d 1.45470 0.02883 50.462 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5874 on 30359 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (30 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 11287 2103.2
## 2 11286 2103.2 1 0.009898 0.0531 0.8177
## model AIC
## 1 1 123636.4
## 2 2 123638.3
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.01701 0.07494 0.227 0.82
## a 21.66715 1.50287 14.417 <2e-16 ***
## b 174.62875 6.69913 26.067 <2e-16 ***
## c 154.79638 10.92491 14.169 <2e-16 ***
## d 1.50194 0.05919 25.375 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4317 on 11287 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7907 2576.2
## 2 7906 2576.1 1 0.0527 0.1617 0.6876
## model AIC
## 1 1 85260.52
## 2 2 85262.36
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.18074 0.11196 -1.614 0.106
## a 16.59776 1.14643 14.478 <2e-16 ***
## b 126.23170 4.51869 27.935 <2e-16 ***
## c 116.00466 5.95712 19.473 <2e-16 ***
## d 1.22690 0.04757 25.791 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5708 on 7907 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13434 2573.5
## 2 13433 2573.5 1 -3.4379e-10 0 1
## model AIC
## 1 1 140618.9
## 2 2 140620.9
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.01578 0.06557 -0.241 0.81
## a 21.63233 1.44962 14.923 <2e-16 ***
## b 109.74919 2.96451 37.021 <2e-16 ***
## c 116.08499 5.44770 21.309 <2e-16 ***
## d 1.44349 0.05263 27.427 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4377 on 13434 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (7 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 19930 6319.4
## 2 19929 6319.4 1 -9.2132e-10 0 1
## model AIC
## 1 1 217248
## 2 2 217250
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.68806 0.07597 9.057 <2e-16 ***
## a 13.36056 0.44646 29.925 <2e-16 ***
## b 144.78186 4.29070 33.743 <2e-16 ***
## c 142.55533 9.68371 14.721 <2e-16 ***
## d 1.87326 0.04721 39.677 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5631 on 19930 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (26 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 20856 9549.0
## 2 20853 9539.3 3 9.7429 7.0994 9.174e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 232202.4
## 2 2 232164.9
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.320e-01 7.386e-02 3.141 0.00169 **
## phi 1.491e-02 5.111e-03 2.917 0.00354 **
## a 1.315e+01 5.339e-01 24.639 < 2e-16 ***
## b 1.650e+02 6.700e+00 24.629 < 2e-16 ***
## c 1.800e+02 1.714e+01 10.502 < 2e-16 ***
## d 1.970e+00 6.150e-02 32.036 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6764 on 20853 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (60 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2184 814.28
## 2 2183 812.63 1 1.6406 4.4072 0.0359 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24930.06
## 2 2 24927.64
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.12750 0.23214 -0.549 0.582893
## phi 0.03866 0.01855 2.085 0.037219 *
## a 18.50507 3.93531 4.702 2.73e-06 ***
## b 249.58616 75.54526 3.304 0.000969 ***
## c 306.23891 190.54750 1.607 0.108166
## d 1.97732 0.35814 5.521 3.77e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6101 on 2183 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.89486, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.753, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 240 60.621
## 2 239 60.621 1 -3.2081e-11 0 1
## model AIC
## 1 1 3071.216
## 2 2 3073.216
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.5603 0.4889 -1.146 0.2529
## a 31.0320 23.7278 1.308 0.1922
## b 615.5216 155.0120 3.971 9.47e-05 ***
## c 352.7609 165.3432 2.134 0.0339 *
## d 1.8421 0.3603 5.113 6.50e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5026 on 240 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96457, p-value = 9.228e-06
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.5226, p-value = 0.0004273
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2779 735.04
## 2 2778 734.99 1 0.053246 0.2013 0.6537
## model AIC
## 1 1 29307.39
## 2 2 29309.19
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.33624 0.15541 -2.164 0.0306 *
## a 27.65434 2.41852 11.434 <2e-16 ***
## b 103.81353 5.49961 18.877 <2e-16 ***
## c 101.68632 6.64390 15.305 <2e-16 ***
## d 1.11177 0.07391 15.042 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5143 on 2779 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96148, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -24.414, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1280 483.88
## 2 1279 483.88 1 0.0040563 0.0107 0.9175
## model AIC
## 1 1 13076.50
## 2 2 13078.49
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.5129 0.2501 -2.050 0.0405 *
## a 14.2442 2.0561 6.928 6.75e-12 ***
## b 83.0909 5.9733 13.910 < 2e-16 ***
## c 69.9975 6.5513 10.685 < 2e-16 ***
## d 1.2098 0.1009 11.991 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6148 on 1280 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94546, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -12.563, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Error in nls(f_ln_1, data = P_261, start = c(ge = ge.start, a = a.start, :
## Convergence failure: singular convergence (7)
## Error in nls(f_ln_2, data = P_261, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: false convergence (8)
## model AIC
## 1 1 NA
## 2 2 NA
## Warning in min(AIC1_261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_261.", Mod.Sel1, sep = "")) :
## object 'nls_261.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## Error in if (any(nEQ <- vNms != make.names(vNms))) vNms[nEQ] <- paste0("`", :
## missing value where TRUE/FALSE needed
## model AIC
## 1 1 NA
## 2 2 NA
## Warning in min(AIC1_262$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_262.", Mod.Sel1, sep = "")) :
## object 'nls_262.' not found
simple model: does not fit
phi model: does not fit
unable to fit model (0 observations)
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 424 97.216
## 2 423 97.216 1 -1.4211e-14 0 1
## model AIC
## 1 1 5410.454
## 2 2 5412.454
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.049e+00 8.421e-01 2.434 0.0154 *
## a 0.000e+00 5.605e+01 0.000 1.0000
## b 1.000e+03 1.104e+03 0.906 0.3656
## c 5.000e+03 1.852e+04 0.270 0.7873
## d 3.487e+00 2.003e+00 1.741 0.0825 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4788 on 424 degrees of freedom
##
## Algorithm "port", convergence message: both X-convergence and relative convergence (5)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96675, p-value = 2.737e-08
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.1995, p-value = 5.664e-10
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 501 172.40
## 2 500 172.39 1 0.014962 0.0434 0.8351
## model AIC
## 1 1 5435.558
## 2 2 5437.514
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.78642 0.35499 -2.215 0.0272 *
## a 25.47377 4.39240 5.800 1.18e-08 ***
## b 110.39796 11.78116 9.371 < 2e-16 ***
## c 131.74298 4.59337 28.681 < 2e-16 ***
## d 0.66796 0.05752 11.613 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5866 on 501 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9006, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.7647, p-value < 2.2e-16
## alternative hypothesis: two.sided
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 747 494.66
## 2 746 494.66 1 -2.7391e-09 0 1
## model AIC
## 1 1 7635.544
## 2 2 7637.544
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.3460 0.5299 -0.653 0.513998
## a 10.0252 2.5769 3.890 0.000109 ***
## b 54.4545 8.0086 6.799 2.15e-11 ***
## c 129.9000 27.9390 4.649 3.94e-06 ***
## d 1.4323 0.2387 6.000 3.08e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8138 on 747 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.86835, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -12.04, p-value < 2.2e-16
## alternative hypothesis: two.sided
* Cannot fit model
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 317 222.58
## 2 316 222.33 1 0.25864 0.3676 0.5447
## model AIC
## 1 1 3495.858
## 2 2 3497.484
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.2643 0.8434 -0.313 0.754
## a 24.2164 15.4301 1.569 0.118
## b 321.7358 2059.4978 0.156 0.876
## c 1383.2317 15422.6995 0.090 0.929
## d 2.3261 4.3085 0.540 0.590
##
## Residual standard error: 0.8379 on 317 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.85367, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -9.0512, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 141 43.589
## 2 140 43.589 1 7.3186e-13 0 1
## model AIC
## 1 1 1561.523
## 2 2 1563.523
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.2044 1.3718 0.878 0.381453
## a 29.3517 8.7951 3.337 0.001082 **
## b 67.9425 18.5935 3.654 0.000363 ***
## c 141.8680 14.2903 9.928 < 2e-16 ***
## d 0.6582 0.1398 4.709 5.88e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.556 on 141 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96506, p-value = 0.0008963
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.3833, p-value = 0.0007162
## alternative hypothesis: two.sided
## Error in nls(f_ln_2, data = P_342, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: singular convergence (7)
## model AIC
## 1 1 3420.252
## 2 2 NA
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.3774 1.2278 0.307 0.758792
## a 16.8483 5.3718 3.136 0.001872 **
## b 48.3460 13.2043 3.661 0.000294 ***
## c 120.4151 12.1849 9.882 < 2e-16 ***
## d 0.8567 0.1812 4.729 3.42e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9198 on 314 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.88507, p-value = 9.49e-15
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -4.8708, p-value = 1.112e-06
## alternative hypothesis: two.sided
## Warning: Removed 1 rows containing missing values (geom_point).
## Warning: Removed 1 rows containing missing values (geom_pointrange).
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 164 71.662
## 2 163 71.662 1 1.5513e-10 0 1
## model AIC
## 1 1 1791.752
## 2 2 1793.752
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.3900 0.5698 -2.439 0.0158 *
## a 11.0691 25.2901 0.438 0.6622
## b 934.1442 6742.0081 0.139 0.8900
## c 5000.0000 75754.5925 0.066 0.9475
## d 3.0309 5.3754 0.564 0.5736
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.661 on 164 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96756, p-value = 0.0005489
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.3815, p-value = 7.387e-08
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 10055 1976.7
## 2 10054 1970.4 1 6.2748 32.018 1.569e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 106916.2
## 2 2 106886.2
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.05650 0.09138 0.618 0.536
## phi 0.02967 0.00544 5.455 5.01e-08 ***
## a 15.08533 1.52106 9.918 < 2e-16 ***
## b 154.85207 6.93604 22.326 < 2e-16 ***
## c 186.83134 15.64827 11.939 < 2e-16 ***
## d 1.58443 0.06894 22.982 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4427 on 10054 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 13158 2159.7
## 2 13157 2159.7 1 0 0 1
## model AIC
## 1 1 145111.3
## 2 2 145113.3
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.66998 0.07326 9.145 <2e-16 ***
## a 27.60308 1.42684 19.346 <2e-16 ***
## b 127.24722 2.60234 48.897 <2e-16 ***
## c 107.28587 3.05414 35.128 <2e-16 ***
## d 1.35134 0.03717 36.352 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.4051 on 13158 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (2 observations deleted due to missingness)
## Error in nls(f_ln_1, data = P_M223, start = c(ge = ge.start, a = a.start, :
## Convergence failure: iteration limit reached without convergence (10)
## Error in nls(f_ln_2, data = P_M223, start = c(ge = ge.start, phi = phi.start, :
## Convergence failure: iteration limit reached without convergence (10)
## model AIC
## 1 1 NA
## 2 2 NA
## Warning in min(AIC1_M223$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_M223.", Mod.Sel1, sep = "")) :
## object 'nls_M223.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot observed vs. predicted"
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1482 342.11
## 2 1481 341.16 1 0.94375 4.0968 0.04314 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 15289.65
## 2 2 15287.55
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.658e-01 2.521e-01 0.658 0.5108
## phi 3.674e-02 1.853e-02 1.983 0.0475 *
## a 3.215e+00 4.266e+00 0.754 0.4512
## b 2.277e+02 1.231e+02 1.850 0.0646 .
## c 8.349e+02 1.151e+03 0.725 0.4684
## d 2.737e+00 7.004e-01 3.908 9.72e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.48 on 1481 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96879, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -18.544, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7932 4824
## 2 7931 4824 1 -1.0768e-09 0 1
## model AIC
## 1 1 105695.1
## 2 2 105697.1
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 8.961e-03 1.632e-01 0.055 0.956
## a 0.000e+00 7.564e+00 0.000 1.000
## b 5.220e+02 4.142e+01 12.603 < 2e-16 ***
## c 8.633e+02 1.940e+02 4.449 8.74e-06 ***
## d 2.514e+00 1.750e-01 14.370 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7799 on 7932 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
## Warning in log(STDAGE/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Warning in log(STDAGE/c): NaNs produced
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 1 NA
## 2 2 NA
## Warning in min(AIC1_M261$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf
## Error in get(paste("nls_M261.", Mod.Sel1, sep = "")) :
## object 'nls_M261.' not found
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## [1] "cannot plot data with prediction"
## [1] "cannot plot residuals"
## [1] "cannot plot data with prediction"
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 907 273.82
## 2 906 273.21 1 0.60241 1.9976 0.1579
## model AIC
## 1 1 9513.399
## 2 2 9513.390
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.82619 0.28070 -2.943 0.00333 **
## phi 0.02915 0.01893 1.540 0.12387
## a 25.27188 5.34178 4.731 2.59e-06 ***
## b 111.54653 10.25159 10.881 < 2e-16 ***
## c 150.89398 11.70684 12.889 < 2e-16 ***
## d 0.84635 0.09253 9.147 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5491 on 906 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.94701, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -7.9897, p-value = 1.353e-15
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 5204 1792.8
## 2 5203 1792.8 1 0.000435 0.0013 0.9717
## model AIC
## 1 1 54507.6
## 2 2 54509.6
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.98350 0.09788 -10.05 <2e-16 ***
## a 23.84555 1.53003 15.59 <2e-16 ***
## b 132.20661 6.39948 20.66 <2e-16 ***
## c 257.07744 23.79494 10.80 <2e-16 ***
## d 1.45077 0.08268 17.55 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.5869 on 5204 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (27 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6770 3131.6
## 2 6769 3119.2 1 12.359 26.821 2.297e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 73749.96
## 2 2 73725.17
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.126e-01 1.878e-01 2.197 0.0281 *
## phi 4.961e-02 8.995e-03 5.516 3.6e-08 ***
## a 1.625e+01 9.543e-01 17.027 < 2e-16 ***
## b 1.072e+02 4.832e+00 22.194 < 2e-16 ***
## c 2.120e+02 1.160e+01 18.278 < 2e-16 ***
## d 1.376e+00 5.654e-02 24.341 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6788 on 6769 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (5 observations deleted due to missingness)
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4432 1818.5
## 2 4431 1813.3 1 5.2046 12.718 0.000366 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 49380.46
## 2 2 49369.75
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.38596 0.22716 1.699 0.089375 .
## phi 0.03892 0.01063 3.663 0.000252 ***
## a 18.80827 1.08906 17.270 < 2e-16 ***
## b 130.47290 6.45246 20.221 < 2e-16 ***
## c 137.56631 4.44177 30.971 < 2e-16 ***
## d 1.09670 0.03414 32.122 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6397 on 4431 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (3 observations deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93137, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -19.315, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 710 277.98
## 2 709 276.92 1 1.0638 2.7236 0.09932 .
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 7186.079
## 2 2 7185.338
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) *
## (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -3.341e-01 3.837e-01 -0.871 0.384
## phi 3.183e-02 1.948e-02 1.634 0.103
## a 5.701e+00 2.127e+01 0.268 0.789
## b 1.894e+02 5.143e+02 0.368 0.713
## c 5.000e+03 4.717e+04 0.106 0.916
## d 3.745e+00 4.918e+00 0.761 0.447
##
## Residual standard error: 0.625 on 709 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95662, p-value = 1.105e-13
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -8.8529, p-value < 2.2e-16
## alternative hypothesis: two.sided
## Analysis of Variance Table
##
## Model 1: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Model 2: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (a + b * exp(-((log(STDAGE/c))/d)^2))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 486 175.73
## 2 485 175.73 1 -1.6266e-10 0 1
## model AIC
## 1 1 4974.722
## 2 2 4976.722
##
## Formula: BIO_MgHa ~ (1 + (MEASTIME - 1990) * ge/100) * (a + b * exp(-((log(STDAGE/c))/d)^2))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.3835 0.2579 -5.364 1.26e-07 ***
## a 18.5217 3.1507 5.879 7.70e-09 ***
## b 111.2733 12.4104 8.966 < 2e-16 ***
## c 220.2789 41.6622 5.287 1.88e-07 ***
## d 1.3201 0.1853 7.123 3.83e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6013 on 486 degrees of freedom
##
## Algorithm "port", convergence message: relative convergence (4)
## (1 observation deleted due to missingness)
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90332, p-value < 2.2e-16
##
##
## ------
##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.1527, p-value = 2.567e-07
## alternative hypothesis: two.sided
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 2 |
| 212 | Laurentian Mixed Forest | 2 |
| 221 | Eastern Broadleaf Forest | 1 |
| 222 | Midwest Broadleaf Forest | 1 |
| 223 | Central Interior Broadleaf Forest | 1 |
| 231 | Southeastern Mixed Forest | 1 |
| 232 | Outer Coastal Plain Mixed Forest | 2 |
| 234 | Lower Mississippi Riverine Forest | 2 |
| 242 | Pacific Lowland Mixed Forest | 1 |
| 251 | Prairie Parkland (Temperate) | 1 |
| 255 | Prairie Parkland (Subtropical) | 1 |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | 1 |
| 313 | Colorado Plateau Semi-Desert | 1 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | 1 |
| 332 | Great Plains Steppe | 1 |
| 341 | Intermountain Semi-Desert and Desert | 1 |
| 342 | Intermountain Semi-Desert | 1 |
| 411 | Everglades | 1 |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 2 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 1 |
| M223 | Ozark Broadleaf Forest Meadow | NA |
| M231 | Ouachita Mixed Forest | 2 |
| M242 | Cascade Mixed Forest | 1 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 2 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 1 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 2 |
| M334 | Black Hills Coniferous Forest | 2 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | 1 |
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | a | a.2.5 | a.97.5 | b | b.2.5 | b.97.5 | c | c.2.5 | c.97.5 | d | d.2.5 | d.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 9943 | 3257 | -0.2412335 | -0.4497812 | -0.0326858 | 0.0481211 | 0.0355012 | 0.0607409 | 28.841474 | 26.469998 | 31.21295 | 131.42371 | 122.90701 | 139.94042 | 126.03678 | 115.50692 | 136.56663 | 1.1023765 | 1.0234745 | 1.1812786 |
| 212 | Laurentian Mixed Forest | east | 30395 | 11945 | 0.1140061 | -0.0127661 | 0.2407784 | 0.0000000 | -0.0060365 | 0.0060365 | 14.452839 | 13.671200 | 15.23448 | 92.71935 | 89.28687 | 96.15183 | 128.41078 | 120.45184 | 136.36973 | 1.4547033 | 1.3981993 | 1.5112073 |
| 221 | Eastern Broadleaf Forest | east | 11294 | 4269 | 0.0170145 | -0.1298727 | 0.1639017 | NA | NA | NA | 21.667151 | 18.721272 | 24.61303 | 174.62875 | 161.49729 | 187.76020 | 154.79638 | 133.38167 | 176.21110 | 1.5019436 | 1.3859194 | 1.6179677 |
| 222 | Midwest Broadleaf Forest | east | 7913 | 3189 | -0.1807390 | -0.4002087 | 0.0387307 | NA | NA | NA | 16.597763 | 14.350454 | 18.84507 | 126.23170 | 117.37387 | 135.08952 | 116.00466 | 104.32712 | 127.68219 | 1.2269038 | 1.1336515 | 1.3201562 |
| 223 | Central Interior Broadleaf Forest | east | 13446 | 4895 | -0.0157796 | -0.1443065 | 0.1127474 | NA | NA | NA | 21.632327 | 18.790866 | 24.47379 | 109.74919 | 103.93832 | 115.56005 | 116.08499 | 105.40672 | 126.76326 | 1.4434940 | 1.3403324 | 1.5466556 |
| 231 | Southeastern Mixed Forest | east | 19961 | 7904 | 0.6880599 | 0.5391543 | 0.8369655 | NA | NA | NA | 13.360558 | 12.485458 | 14.23566 | 144.78186 | 136.37174 | 153.19199 | 142.55533 | 123.57446 | 161.53620 | 1.8732595 | 1.7807183 | 1.9658006 |
| 232 | Outer Coastal Plain Mixed Forest | east | 20919 | 9046 | 0.2319657 | 0.0871922 | 0.3767392 | 0.0149078 | 0.0048896 | 0.0249261 | 13.153721 | 12.107322 | 14.20012 | 165.02420 | 151.89072 | 178.15769 | 180.02788 | 146.42621 | 213.62954 | 1.9703357 | 1.8497826 | 2.0908888 |
| 234 | Lower Mississippi Riverine Forest | east | 2190 | 937 | -0.1275039 | -0.5827497 | 0.3277420 | 0.0386612 | 0.0022919 | 0.0750306 | 18.505068 | 10.787721 | 26.22242 | 249.58616 | 101.43803 | 397.73429 | 306.23891 | -67.43450 | 679.91232 | 1.9773181 | 1.2749868 | 2.6796494 |
| 242 | Pacific Lowland Mixed Forest | pacific | 246 | 172 | -0.5603063 | -1.5232964 | 0.4026838 | NA | NA | NA | 31.031987 | -15.709302 | 77.77328 | 615.52160 | 310.16376 | 920.87944 | 352.76085 | 27.05174 | 678.46997 | 1.8421147 | 1.1323308 | 2.5518985 |
| 251 | Prairie Parkland (Temperate) | east | 2787 | 1036 | -0.3362390 | -0.6409707 | -0.0315074 | NA | NA | NA | 27.654337 | 22.912059 | 32.39661 | 103.81353 | 93.02980 | 114.59726 | 101.68632 | 88.65884 | 114.71380 | 1.1117727 | 0.9668465 | 1.2566990 |
| 255 | Prairie Parkland (Subtropical) | pacific | 1288 | 659 | -0.5128856 | -1.0036203 | -0.0221509 | NA | NA | NA | 14.244225 | 10.210621 | 18.27783 | 83.09090 | 71.37236 | 94.80944 | 69.99751 | 57.14508 | 82.84995 | 1.2098430 | 1.0119033 | 1.4077827 |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 56 | 34 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 430 | 274 | 2.0492815 | 0.3941688 | 3.7043941 | NA | NA | NA | 0.000000 | -110.170512 | 110.17051 | 1000.00000 | -1170.07033 | 3170.07033 | 5000.00000 | -31404.83509 | 41404.83509 | 3.4866144 | -0.4503236 | 7.4235524 |
| 313 | Colorado Plateau Semi-Desert | interior west | 508 | 312 | -0.7864222 | -1.4838778 | -0.0889666 | NA | NA | NA | 25.473773 | 16.843973 | 34.10357 | 110.39796 | 87.25140 | 133.54453 | 131.74298 | 122.71833 | 140.76763 | 0.6679632 | 0.5549576 | 0.7809689 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 16 | 12 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 22 | 14 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 8 | 5 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 753 | 473 | -0.3459760 | -1.3862004 | 0.6942484 | NA | NA | NA | 10.025225 | 4.966406 | 15.08404 | 54.45449 | 38.73241 | 70.17658 | 129.89998 | 75.05163 | 184.74833 | 1.4323237 | 0.9636546 | 1.9009929 |
| 332 | Great Plains Steppe | interior west | 324 | 152 | -0.2642535 | -1.9235370 | 1.3950299 | NA | NA | NA | 24.216351 | -6.142070 | 54.57477 | 321.73583 | -3730.27597 | 4373.74763 | 1383.23171 | -28960.55405 | 31727.01747 | 2.3260724 | -6.1508064 | 10.8029511 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 147 | 93 | 1.2043907 | -1.5075434 | 3.9163248 | NA | NA | NA | 29.351705 | 11.964479 | 46.73893 | 67.94252 | 31.18450 | 104.70055 | 141.86797 | 113.61703 | 170.11891 | 0.6582137 | 0.3819104 | 0.9345170 |
| 342 | Intermountain Semi-Desert | interior west | 320 | 222 | 0.3773512 | -2.0384323 | 2.7931346 | NA | NA | NA | 16.848265 | 6.279003 | 27.41753 | 48.34601 | 22.36602 | 74.32600 | 120.41512 | 96.44070 | 144.38954 | 0.8567007 | 0.5002262 | 1.2131751 |
| 411 | Everglades | east | 170 | 86 | -1.3900149 | -2.5151636 | -0.2648662 | NA | NA | NA | 11.069099 | -38.867171 | 61.00537 | 934.14418 | -12378.18402 | 14246.47237 | 5000.00000 | -144580.06224 | 154580.06224 | 3.0309044 | -7.5829445 | 13.6447533 |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 10063 | 3398 | 0.0564998 | -0.1226288 | 0.2356283 | 0.0296737 | 0.0190109 | 0.0403364 | 15.085331 | 12.103749 | 18.06691 | 154.85207 | 141.25605 | 168.44808 | 186.83134 | 156.15760 | 217.50507 | 1.5844284 | 1.4492894 | 1.7195674 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 13165 | 4970 | 0.6699803 | 0.5263827 | 0.8135780 | NA | NA | NA | 27.603081 | 24.806265 | 30.39990 | 127.24722 | 122.14626 | 132.34818 | 107.28587 | 101.29932 | 113.27242 | 1.3513443 | 1.2784788 | 1.4242098 |
| M223 | Ozark Broadleaf Forest Meadow | east | 1248 | 392 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M231 | Ouachita Mixed Forest | east | 1488 | 574 | 0.1658361 | -0.3286921 | 0.6603644 | 0.0367390 | 0.0003998 | 0.0730783 | 3.214899 | -5.153137 | 11.58293 | 227.73280 | -13.78808 | 469.25369 | 834.90949 | -1423.37455 | 3093.19353 | 2.7372552 | 1.3633988 | 4.1111115 |
| M242 | Cascade Mixed Forest | pacific | 7940 | 4900 | 0.0089612 | -0.3109837 | 0.3289061 | NA | NA | NA | 0.000000 | -14.826575 | 14.82658 | 522.02082 | 440.82731 | 603.21433 | 863.30726 | 482.94235 | 1243.67218 | 2.5141501 | 2.1711867 | 2.8571134 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 4575 | 2761 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 54 | 38 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 913 | 563 | -0.8261935 | -1.3770856 | -0.2753014 | 0.0291549 | -0.0079966 | 0.0663063 | 25.271882 | 14.788180 | 35.75558 | 111.54653 | 91.42690 | 131.66616 | 150.89398 | 127.91830 | 173.86967 | 0.8463537 | 0.6647606 | 1.0279467 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 5236 | 3514 | -0.9834959 | -1.1753756 | -0.7916163 | NA | NA | NA | 23.845553 | 20.846057 | 26.84505 | 132.20661 | 119.66093 | 144.75228 | 257.07744 | 210.42936 | 303.72551 | 1.4507703 | 1.2886900 | 1.6128507 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 6780 | 4293 | 0.4125899 | 0.0444181 | 0.7807617 | 0.0496127 | 0.0319800 | 0.0672454 | 16.248841 | 14.378155 | 18.11953 | 107.24863 | 97.77562 | 116.72164 | 212.02048 | 189.28104 | 234.75992 | 1.3761817 | 1.2653523 | 1.4870111 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 4440 | 2838 | 0.3859621 | -0.0593855 | 0.8313096 | 0.0389236 | 0.0180926 | 0.0597546 | 18.808270 | 16.673165 | 20.94337 | 130.47290 | 117.82286 | 143.12294 | 137.56631 | 128.85822 | 146.27439 | 1.0967019 | 1.0297679 | 1.1636359 |
| M334 | Black Hills Coniferous Forest | interior west | 716 | 364 | -0.3341002 | -1.0873426 | 0.4191422 | 0.0318262 | -0.0064253 | 0.0700776 | 5.701161 | -36.067216 | 47.46954 | 189.39363 | -820.25450 | 1199.04176 | 5000.00000 | -87612.89848 | 97612.89848 | 3.7448342 | -5.9114757 | 13.4011440 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 492 | 287 | -1.3834885 | -1.8902300 | -0.8767470 | NA | NA | NA | 18.521694 | 12.331014 | 24.71237 | 111.27327 | 86.88860 | 135.65793 | 220.27885 | 138.41854 | 302.13916 | 1.3200946 | 0.9559446 | 1.6842445 |
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 8 rows containing missing values (geom_point).
## Warning: Removed 12 rows containing missing values (geom_point).
## Warning: Removed 8 rows containing missing values (geom_point).
## region weighted.ge
## 1 entire US 0.11435795
## 2 pacific 0.01943735
## 3 east 0.18894294
## 4 interior west -0.13858977
## region weighted.phi
## 1 entire US 0.010287666
## 2 pacific 0.000000000
## 3 east 0.008045572
## 4 interior west 0.026665510
## region weighted.ge
## 1 entire US 0.202434442
## 2 pacific 0.005731607
## 3 east 0.213926432
## 4 interior west 0.412589912
## region weighted.phi
## 1 entire US 0.01026246
## 2 pacific 0.00000000
## 3 east 0.00854629
## 4 interior west 0.04961268